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Question
A simple harmonic oscillator has amplitude A, angular velocity ω and mass m. Then, average energy in one time period will be ______.
Options
`1/4"m"omega^2"A"^2`
`1/2"m"omega^2"A"^2`
`"m"omega^2"A"^2`
zero
MCQ
Fill in the Blanks
Solution
A simple harmonic oscillator has amplitude A, angular velocity ω and mass m. Then, average energy in one time period will be `bbunderline(1/4"m"omega^2"A"^2)`.
Explanation:
Average energy = `(int_0^"T""udt")/(int_0^"T""dt")=1/"T"int_0^"T""udt"`
= `1/(2"T")int_0^"T""m"omega^2"A"^2cos^2(omega"t" + phi)"dt"`
= `1/4"m"omega^2"A"^2`
shaalaa.com
The Energy of a Particle Performing S.H.M.
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